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Interpretation/logic/Mates: an interpretation assigns: individual constants: individuals - one-digit predicates: properties (classes of individuals) - two-digit predicates: relations - statement letter: truth values - truth values come into play when the logical constants are interpreted.
Truth values: may change when we pass from one interpretation to another, without the form of the statement being changed - the terms "true" and "valid" refer to all interpretations of a particular type.
A statement is always true in relation to an interpretation.
Interpretation/QL/Mates: if quantifiers have to be considered, we need a helping concept. We need two interpretations I and I"- b: is an individual constant - then b-variant - the interpretations then differ at the most in what they assign to b ("at most to b-th place").
Then has the substitution y"(namely y a/b) a specific truth value at every interpretation.
Complete interpretation: not desirable because we also examine statements, where not names for all individual constants are available - e.g. real numbers.
Interpretation/translation/truth/intention/artificial language/Mates. Problem: The interpretation also has a "manner of being given". E.g. "2" as the "smallest prime" or "only even prime number" - translation: not unambigiuous - solution. helping concept: "predicate of the German language" - Problem: no systematic rules - meaning/everyday language: depends on the context.
Interpretation specifies truth conditions (WB) fixed - truth condition: Then here in German. - With that it will give every statement a meaning.
Interpretation/logic/Mates. would there be a complete I, then scheme: (W) X is only true if and only then at I when p - although the truth conditions are in German.
Elementare Logik Göttingen 1969